why does (-5)*(-4)=20 ?, eom

[Aractus]

Perhaps some of you idiots should try explaining if you really do know the reason that two negatives multiplied together give a positive.

I'll give you my take on it - mathematics is invented by humans, and is based on rules, which are also invented. Numbers are not real, and while positive numbers can be likened to reality, somewhat, negative numbers of course cannot. For instance you can 0 Apples, you can 12 Apples, but you can not have -1 Apples. The reason we have negative numbers is that that we can perform negative operations on positive numbers, for instance if you have 12 Apples and negative 9 Apples you now have 3 Apples. Note that you cannot physically have 12 Apples and negative 13 Apples, however you can do this in mathematics. Each integer and each rational number has a negative inverse, which when added together equals zero. For instance 5 + (-5) = 0.

Anyway, the rules are this:

1 * -1 = -1

Now divide each side by -1 (you can just remove it from the left side):

1 = -1/-1

So two negatives divided by each other equal a positive, and the same must be true for multiplication because you can rewrite it like this:

1 = (1/-1) * (-1/1)
1 = -(1/1) * -(1/1)
1 = -1 * -1

That's one reason, and the only other reason I can think of, and it may be the more correct reason, is that -1*-1 = +1 is the only way to solve the equation without causing other mathematical problems and issues with negative numbers. For instance, if -1 * -1 = -1 and +1 * +1 = +1, then how do you transform a negative number into a positive? You can't, but you can transform a positive number into a negative like this: +1 * -1 = -1, so it would have no inverse there would be no way in which to undo it. Another rule that would break is this one - any number "k" divided by itself equals 1 ie k/k = 1, well if -1 * -1 = -1 then for k= -1: -1 / -1 = -1, rule broken!